Solving and analyzing the geodesic equation gives the dynamics of equation of motion of the system. For example, the famous case of the precession of the perihelion of Mercury [1]}, [2]}. Solving the geodesic deviation equation (acceleration equation) enables one to understand the equation of motion of nearby test-particles under gravitational effect. For example, solving the linearlized, weak-field limit equation gives the gravitational wave solution [3]}, [4]}.
